What is the time complexity of the dynamic programming solution for the 0/1 Knapsack problem?
Practice Questions
1 question
Q1
What is the time complexity of the dynamic programming solution for the 0/1 Knapsack problem?
O(n)
O(n^2)
O(n * W)
O(2^n)
The time complexity of the dynamic programming solution for the 0/1 Knapsack problem is O(n * W), where n is the number of items and W is the maximum weight capacity.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the time complexity of the dynamic programming solution for the 0/1 Knapsack problem?
Solution: The time complexity of the dynamic programming solution for the 0/1 Knapsack problem is O(n * W), where n is the number of items and W is the maximum weight capacity.
Steps: 6
Step 1: Understand the 0/1 Knapsack problem. It involves selecting items with given weights and values to maximize value without exceeding a weight limit.
Step 2: Identify the variables involved. Let 'n' be the number of items and 'W' be the maximum weight capacity of the knapsack.
Step 3: Recognize that the dynamic programming approach uses a table to store solutions to subproblems. The table has dimensions (n+1) x (W+1).
Step 4: Realize that filling this table requires iterating through each item (n) and each weight capacity (W).
Step 5: Calculate the total number of operations. For each item, you check all weight capacities, leading to n * W operations.
Step 6: Conclude that the time complexity of the dynamic programming solution is O(n * W).
